okie... not sure how much I would be help of, as am a newbie for syncsort... let's try...

What I think a solution to the problem can be to filter records in temporary datasets for weekly basis and then count records from the temp file.

Now is there any constraint, that you would/wouldn't get a fix number of weeks in the input file.
Looking at the example it looks like, you are counting a week of 5 days, is that the understanding ?
We can hardcode values of date to be checked in condition, but this would be changing for weeks every next month.